Calculators

As many of you know, I have strong views about using a calculator for studying.
My personal opinion is that when given the option, many students rush to the calculator too often. I saw students using a calculator for a (very) simple addition problem, or for solving a term that by simplifying it a little bit they would realize that they could bring it down to a simple answer (like 4*6/12). I encourage all my students to try and solve a question first in their heads or on a piece of paper before pulling out the calculator. Beyond improving their abilities to do more math in their heads, I often see the calculator having the exact opposite of it's intended effect - it wastes time instead of saving it. Take for example the previous example I gave - 4*6/12 . Many students get confused or scared by it's appearance and rush to the calculator to do the following - take the calculator from it's case, open it, punch in the first term (4*6), press Enter, type the result in the next term (24/12), press Enter again, and copy the answer to the page. Often that would take longer then just realizing that 4*6 is a multiple of 12, or even that 6/12 is actually 1/2 which means the term reduces to 4/2 . 
That said, I do see a lot of value in using a calculator in certain situations, especially a graphing calculator. When I was in high school, I took the American AP exam the first year calculators were allowed for it. I learned to love my TI-85 (since replaced by the TI-84 plus). It was in many ways my first handheld computer. I used it for my math and science course, I used to write games and programs for it using it's internal programming features. I once made a presentation in my high school ECON class using the calculator to simulate an economic trend. I used it to store equations, formulas, to do advance graphing, complex multi-variable equation solving and more, all through my first couple of years in university. It was a wonderful tool.
I see the value of using a calculator (for courses where it's allowed during exams), and I do recommend using the calculator for difficult calculations. When is a problem too complicated for pen-brain-paper? that's a personal questions. I believe everyone has a cognitive virtual boundary for when they are better off, time wise, turning to their calculator. Some people will do it for 4*9, some for 4*19, some only for something like 7%*17. I understand that. I just also believe that whatever your boundary is, you should always try to push it, and when I have students who rushes too fast (relative to my perception of their ability) to the calculator, i'll usually stop them and ask them to look at the problem first and try to solve it without the calculator. In effect, i'm getting them to push their own boundary forward, in order for them to be able to do  more calculations faster which will translate to more time in an exam.
On the other extreme, I see students struggle with their calculators too hard sometimes. A classic example is a student who takes close to half a minute to punch into her graphing calculator something like (4*5^2)+7^2 . Here the problem is that she is probably too used to a simple calculator and breaks the term to several basic ones (5^2 , 4*25, 7^2, 100+49) instead of just writing it out once. I also see students struggle with using graphs with their TI calculators, sometimes not knowing how to trace a simple graph, let alone use the calculator to find an interception between two lines. I try to help as much as I can, and teach calculator techniques (use the 2nd-trace options for graphs) as well as tricks (you don't need the final closing bracket, store often used terms in built-in variables), and functions (use 'solve' to find roots for functions). But my best and often given advice has always been - take the time to know your calculator, that time will pay itself back several times over during homework and especially exam time. I can't stress that enough. Just like you are more likely to make the most of your cellphone by reading (even a little bit) about what it can do, so are you ever so likely to improve you test score (or at least your time) by knowing what your calculator can do.
Just in case the instruction booklet and CD is either buried under an unknown Himalayan pile in your room, or long recycled, here are links to the manuals of the most popular graphing calculators - the TI-83 (Plus and Plus Silver) and the TI-84 (Plus and Plus Silver) (i'll put the files on my website once it's done). It shouldn't take more than 30 minutes to go through a whole chapter (like the one about graphs), but boy is it worth it.
Successful Learning!
Amir 


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